Electron. J. Diff. Equ., Vol. 2016 (2016), No. 79, pp. 1-24.

Ergodicity of the two-dimensional magnetic Benard problem

Kazuo Yamazaki

We study the two-dimensional magnetic Benard problem with noise, white in time. We prove the well-posedness including the path-wise uniqueness of the generalized solution, and the existence of the unique invariant, and consequently ergodic, measure under random perturbation.

Submitted December 3, 2015. Published March 16, 2016.
Math Subject Classifications: 35Q35, 37H99, 60H15.
Key Words: Benard problem; ergodicity; invariant measure; irreducibility; Krylov-Bogoliubov theorem; strong Feller.

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Kazuo Yamazaki
Department of Mathematics and Statistics
Washington State University
Pullman, WA 99164-3113, USA
email: kyamazaki@math.wsu.edu, Phone 509-335-9812

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